Question

9. Rút gọn các biểu thức sau

A= cos7x - cos8x - cos9x + cos10x / sin7x - sin8x - sin9x + sin10x

B = sin2x + 2sin3x + sin4x / sin3x +2sin4x + sin5x

C= 1+cosx + cos2x + cos3x / cosx + 2cos^2 . x -1

D = sin4x + sin5x + sin6x / cos4x + cos5x + cos6x

Answer 1

\(D=\frac{sin4x+sin5x+sin6x}{cos4x+cos5x+cos6x}\)

\(=\frac{\left(sin4x+sin6x\right)+sin5x}{\left(cos4x+cos6x\right)+cos5x}\)

\(=\frac{2sin\frac{4x+6x}{2}.cos\frac{4x-6x}{2}+sin5x}{2cos\frac{4x+6x}{2}.cos\frac{4x-6x}{2}+cos5x}\)

\(=\frac{2sin5x.cos\left(-x\right)+sin5x}{2cos5x.cos\left(-x\right)+cos5x}=\frac{sin5x\left(2.cos\left(-x\right)+1\right)}{cos5x\left(2.cos\left(-x\right)+1\right)}=\frac{sin5x}{cos5x}=tan5x\)